Chapter 3, Problem 6RE

(a)

To determine

the slope and y-intercept of each linear function.

Answer to Problem 6RE

Slope $m=0$ and y intercept, $b=-3$ .

Explanation of Solution

Given:

  $H\left(x\right)=-3$ .

Calculation:

The slope intercept form of a line is $y=mx+b$ ,

Where the slope of the line is m ,

And y intercept is b .

Compare the function $H\left(x\right)=0.x-3$ with slope intercept form,

Slope $m=0$ and y intercept, $b=-3$ .

Conclusion:

Therefore, the slope $m=0$ and y intercept, $b=-3$ .

(b)

To determine

To find: the average rate of change of each function.

Answer to Problem 6RE

The average rate of change is 0

Explanation of Solution

Calculation:

For calculating average rate of change of the function $H\left(x\right)=-3$ , it is needed two points. Y intercept $\left(0,-3\right)$ is one point and for second point

Let $x=1$ ,

  $\begin{array}{c}H\left(1\right)=0\times 1-3\\ =0-3\\ =-3\end{array}$

So second point in $\left(x,y\right)$ form is $\left(1,3\right)$ .

Now as rate of change $\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Here $x_1=0,y_1=-3,x_2=1,y_2=-3$

So rate of change $=\frac{-3-\left(-3\right)}{1-0}$

  $\begin{array}{c}=\frac{-3+3}{1}\\ =\frac{0}{1}\\ =0\end{array}$

Conclusion:

The average rate of change is 0

(c)

To determine

To graph: the given function

Answer to Problem 6RE

  

Explanation of Solution

Calculation:

The line joining two points $\left(0,-3\right)$ and $\left(1,3\right)$ is shown below where there is no x intercept:

  

Conclusion:

Thus, the graph is drawn.

(d)

To determine

whether the function is increasing, decreasing, or constant

Answer to Problem 6RE

Thus function is Constant

Explanation of Solution

Calculation:

As the slope of the function $H\left(x\right)=-3$ is 0, that means it is a constant function, parallel to x axis.

Thus function is Constant in the interval $\left[-\infty ,+\infty \right]$ .

Conclusion:

Thus function is Constant